8 UH⠀⠀ 5 10 Let v₁ = 1 -1 Choose the correct answer below. and w= 5 5 Is w in the subspace spanned by {V₁, V₂, V3}? Why? 1. O A. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3. 1¹ B. Vector w is not in the subspace spanned by {V₁, V₂, V3) because the equation x₁v₁ + X₂V₂ + X3 V3 = w has no solution which can be seen because an echelon form of the augmented matrix of the system has a row of the form [0... 0 b] with b * 0. =W C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system X₁ V₁ + x₂ V₂ + x3 V3 = is not a pivot column. D. Vector w is in the subspace spanned by {V₁, V2, V3} because the subspace generated by V₁, V₂, and v3 is R³.
8 UH⠀⠀ 5 10 Let v₁ = 1 -1 Choose the correct answer below. and w= 5 5 Is w in the subspace spanned by {V₁, V₂, V3}? Why? 1. O A. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3. 1¹ B. Vector w is not in the subspace spanned by {V₁, V₂, V3) because the equation x₁v₁ + X₂V₂ + X3 V3 = w has no solution which can be seen because an echelon form of the augmented matrix of the system has a row of the form [0... 0 b] with b * 0. =W C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system X₁ V₁ + x₂ V₂ + x3 V3 = is not a pivot column. D. Vector w is in the subspace spanned by {V₁, V2, V3} because the subspace generated by V₁, V₂, and v3 is R³.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
B1.
Advance maths
![4
8
UH⠀⠀
5
10
Let v₁ =
1
-1
Choose the correct answer below.
and w=
5
5
Is w in the subspace spanned by {V₁, V₂, V3}? Why?
1.
O A. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3.
1¹
B. Vector w is not in the subspace spanned by {V₁, V₂, V3) because the equation x₁v₁ + X₂V₂ + X3 V3 = w has no solution which can be seen
because an echelon form of the augmented matrix of the system has a row of the form [0... 0 b] with b * 0.
=W
C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system X₁ V₁ + x₂ V₂ + x3 V3 =
is not a pivot column.
D. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2dbf05e8-4609-48ee-b8a3-5dc8c1c2617c%2F848b7ab3-1390-4736-b739-fffbf508428d%2Fmskkgzc_processed.png&w=3840&q=75)
Transcribed Image Text:4
8
UH⠀⠀
5
10
Let v₁ =
1
-1
Choose the correct answer below.
and w=
5
5
Is w in the subspace spanned by {V₁, V₂, V3}? Why?
1.
O A. Vector w is in the subspace spanned by {V₁, V₂, V3} because w is a linear combination of V₁, V₂, and V3.
1¹
B. Vector w is not in the subspace spanned by {V₁, V₂, V3) because the equation x₁v₁ + X₂V₂ + X3 V3 = w has no solution which can be seen
because an echelon form of the augmented matrix of the system has a row of the form [0... 0 b] with b * 0.
=W
C. Vector w is not in the subspace Span{V₁, V₂, V3} because the rightmost column of the augmented matrix of the system X₁ V₁ + x₂ V₂ + x3 V3 =
is not a pivot column.
D. Vector w is in the subspace spanned by {V₁, V₂, V3} because the subspace generated by V₁, V₂, and v3 is R³.
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